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Math Help - one to one function with unknown constant!

  1. #1
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    one to one function with unknown constant!

    This problem is driving me crazy.

    Let f(x)= 3x^3 + kx^2 +5x, k is a constant. For what values of k is f one to one?

    I tried using b^2 -4ac from the Quadratic Formula but I didn't get the same answer as the answer choices...
    a. |k| <= 3 root5
    b. 5/9 <= k
    c. |k|<= 6 root5
    d. k <= 5/9
    e. 3 root5 <= |k|

    please help
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  2. #2
    GAMMA Mathematics
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    A function f(x) is one-to-one if and only if f(x) has an inverse. Another way to determine if a function f(x) is one-to-one is to test values, therefore if for every a and b in its domain, f(a) = f(b) implies a = b.
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  3. #3
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    Quote Originally Posted by runner07 View Post
    Let f(x)= 3x^3 + kx^2 +5x, k is a constant. For what values of k is f one to one?
    Consider the derivative f'(x) = 9x^2  + 2kx + 5.
    What are the values for k making that derivative nonnegative?
    Why does that work?
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